1
GATE CSE 1997
MCQ (Single Correct Answer)
+2
-0.6
Let $$f\left( {x,y,z} \right) = \overline x + \overline y x + xz$$ be a switching function. Which one of the following is valid?
A
$$\overline y x$$ is a prime implicates of $$f$$
B
$$xz$$ is a minters of $$f$$
C
$$xz$$ is an implicant of $$f$$
D
y is a prime applicant of $$f$$
2
GATE CSE 1997
MCQ (Single Correct Answer)
+2
-0.6
Consider the logic circuit shown in Figure below. The functions $${f_1},$$ $${f_2}$$ and $$f$$ (in canonical sum of products form in decimal notation) are: GATE CSE 1997 Digital Logic - Boolean Algebra Question 35 English

$${f_1}\left( {w,\,x,\,y,\,z} \right) = \sum {8,9,10} $$
$${f_2}\left( {w,\,x,\,y,\,z} \right) = \sum {7,8,12,13,18,15} $$
$$f\left( {w,\,x,\,y,\,z} \right) = \sum {\left( {8,9} \right)} $$

The function $${f_3}$$ is

A
$$\sum {9,\,10} $$
B
$$\sum 9 $$
C
$$\sum {1,8,9} $$
D
$$\sum {8,10,15} $$
3
GATE CSE 1997
MCQ (Single Correct Answer)
+1
-0.3
The probability that it will rain today is 0.5. The probability that it will rain tomorrow is 0.6. The probability that it will rain either today or tomorrow is 0.7. That is the probability that it will rain today and tomorrow?
A
0.3
B
0.25
C
0.35
D
0.4
4
GATE CSE 1997
MCQ (Single Correct Answer)
+1
-0.3
The number of equivalence relations on the set $$\left\{ {1,2,3,4} \right\}$$ is
A
$$15$$
B
$$16$$
C
$$24$$
D
$$4$$
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